Piezoelectric apparatus



May 9, 1939. s. c. HIGHT PIEZOELECTRIG APPARATUS Filed May 19, 1936 2 Sheets-Sheet 1 FIG. 4

INVENTOR By SCH/6H7 ATTORNEY Patented May 9, 1939 UNITED STATES PATENT OFFICE PIEZOELECTRIC APPARATUS Application May 19, 1936, Serial No. 80,513

13 Claims.

This invention relates to piezoelectric apparatus and particularly to piezoelectric crystals suitable for use as circuit elements in oscillation generator systems and in electric wave filter systems, for example.

One of the objects of this invention is to produce a piezoelectric crystal element that may have substantially zero or other desired predetermined temperature coefficient of oscillation frequency either positive or negative and that may be of a convenient size and shape and yet have a relatively low frequency vibration in the range from 30 to 1000 kilocycles per second, for example.

Another object of this invention is to produce a piezoelectric body that may have a frequency substantially independent of changes in temperature over a substantial range of temperatures to permit temperature regulating apparatus to be simplified or eliminated and to permit a constant vibration frequency to be maintained.

Another object of this invention is to obtain for a piezoelectric body a predetermined temperature coefiicient of frequency that may have a positive, negative or zero value.

Another object of this invention is to increase the piezoelectric activity of a crystal oscillator.

It is well known that a quartz oscillator may produce an oscillation of fairly constant frequency and yet there may exist various factors affecting the constancy of oscillation frequency. Among them, the variation of the operating temperature of the crystal is an important factor. It is desirable therefore to obtain a crystal having its oscillation frequency independent of the temperature variation.

In accordance with this invention, the temperature coefficient of frequency of a piezoelectric crystal may be made to pass through zero or go to a positive value. The zero temperature coefiicient of frequency may be obtained accurately enough for frequency standard purposes. This result may be obtained by a suitable selection of the orientation, shape, ratio of dimensions and mode of vibration of the crystal.

In a particular embodiment, the crystal may be in the shape of a rectangular parallelepiped having its longest or major axis dimension substantially perpendicular to an electric or X axis thereof and inclined with respect to the mechanical or Y axis at an angle between about +5 degrees and +20 degrees or preferably about +10 degrees. The dimensional ratios of width to length and of thickness to length may be adjusted to proper values and the crystal operated in a suitable mode of vibration to obtain the zero value of temperature coefiicient of frequency. The mode of vibration may be of longitudinal type at the fundamental or at a harmonic frequency along the longest dimension of the crystal to obtain the zero temperature coefficient of frequency. The 5 harmonic frequency may be the second, third, or fourth harmonic, for example. The second harmonic longitudinal vibration in the Y direction of the crystal provides a very active piezoelectric oscillator. The harmonic vibration may be obtained by a suitable number of pairs of interconnected electrodes corresponding in number of pairs to the order of the selected harmonic.

For a clearer understanding of the nature of this invention and the additional features and objects thereof, reference is made to the follow ing description taken in connection with the accompanying drawings, in which like reference characters represent like or similar parts and in which: 20

Fig. l is a side View of crystal apparatus embodying this invention;

Fig. 2 is a perspective view of the crystal apparatus illustrated in Fig. 1;

Fig. 3 is a topview of the crystal apparatus d illustrated in Fig. 1 adapted to control the frequency of an oscillation generator connected in circuit therewith;

Figs. 4, 5 and 6 are respectively top, elevation and end views of a holder suitable for mounting the crystal illustrated in Figs. 1 to 3;

Figs. '7, 8 and 9 are views of another form of holder and electrodes suitable for mounting the crystal illustrated in Figs. 1 to 3;

Fig. 10 is a graph showing the values of temperature coeflicient of frequency of particular quartz crystals having selected dimensional ratios;

Fig. 11 is a graph showing the values of fre quency constant of particular crystals having selected dimensional ratios; and

Fig. 12 is a graph showing values of temperature coefficient of frequency and of frequency for particular crystals embodying this invention.

This specification will follow the standard terminology as applied to quartz which employs orthogonal X, Y and Z axes to designate the electric, the mechanical and the optic axes respectively of the piezoelectric crystal material and Which employs X, Y and Z to designate the directions of axes or surfaces of a piezoelectric body angularly oriented with respect to the orthogonal X, Y and Z axes thereof. Where the orientation is obtained by rotation about an electric or X axis as particularly illustrated herein, the orientation angle 9 designates the effective angular position of the crystal in degrees as measured from the mechanical or Y axis.

The dimensional ratio herein particularly illustrated, represents the dimensional ratio of thickness X'in the direction of the X or electric axis of the crystal with respect to the length Y or longest axis in the direction of the Y axis; and the dimensional ratio represents the dimensional ratio of width Z in the direction of the Z axis with respect to the length in the direction of the Y axis.

Quartz crystals may occur in two forms, namely, right-hand and left-hand. A crystal is designated as right-hand if it rotatesthe plane of polarization of plane polarized light traveling alongthe'optic or Z axis in a clockwise direction when facing in the direction of propagation of the light'and is designated as left-hand if it rotates the plane of polarization in the counter-clockwise direction. If a compressional stress be applied to the ends of the electric axis of a quartz crystal body and not removed, a charge will be developed which is positive at the positive end of the electric axis and negative at the negative end of the electric axis for either right-hand or left-hand crystals. The magnitude and sign of the charge may be measured with a vacuum tube electrometer, for example. In specifying the orientation of the right-hand crystal, the angle 9 which the new axis Z makes with the optic axis Z as the crystal plate is rotated about the electric axis X is deemed positive when, with the positive end of the X axis pointed toward'the observer, the rotation is in a clockwise direction. A counterclockwise rotation of such a crystal gives rise to a negative orientation angle. Conversely, the orientation angle of a left-hand'crystal is positive when, with the positive 'end of the electric axis X pointed toward the observer, the rotation is counter-clockwise and is negative when the rotation is clockwise. In one species of the invention as applied to quartz, the principal axis of'the crystalis perpendicular'to an X or electric axis thereof and is oriented or inclined at a positive angle of approximately +10 degrees with respect to the mechanical axisthereof. In other species the principal axis may'beTinclinedat an angle between +5 and +20 degrees with respect to the mechanical or .Y axis.

Referring to the drawings, Figs. 1 to 3 illustrate a right-hand piezoelectric quartz crystal l of substantially rectangular parallelepiped shape having its length dimension or longest axis Y disposed substantially perpendicular to an 'X or electric axis thereof and inclined substantially 9=+10 degrees with respect to the mechanical or Y thereof. 'The width dimension Z of the crystal l is, disposed substantially perpendicular to the electric axis X and is axially inclined e=+10 degrees with respect to the optic axis Z of the crystal l as illustratedin Fig. 1. In Fig. 1, the electric axis X is perpendicular to the plane of the drawing with the +X axis directed or projected into the plane of the paper. In Fig. 3, the electric axis X of the crystal l is parallel to the plane of the drawing and extends in the direction of the thickness dimension of the crystal I as indicated in Fig. 2. The crystal l is accordingly for example.

Twopairs of opposite electrodes ID to l3, one pair being the opposite electrodes l0 and II and the otherpair being the opposite electrodes l2 and i3, may be interconnected by suitable conductive connectors as the connectors I5 and 16 illustrated inFigj- 3, for example, and utilized to apply an electric field to the crystal l in the direction of the electric axis X to excite the second harmonic of the longitudinal mode ofvibration substantially in the direction of the length axis Y of the crystal l.

The four electrodes ll} toi3 may be. flat plates of stainless steel or other suitable conductive material disposed on'or adjacent the two opposite surfaces of the crystali; or-alternativelythe electrodes 10 to H3 may be aluminum or other suitable metallic'plating intimately adhering to and integral with the two opposite surfaces, as shown, of the crystal l.

The connector i5 interconnecting the electrodes H and I2 and the connector 16 interconnecting the electrodes Ill and-l-i-are illustrated in :Fig. 3 as Wire connectors but it will be understood'that they may be of any-suitable constructionsuchas, for example, metallic plating integral with the surfaces of the crystal I.

Conductive connectors: l8.andl9 connected respectively with he'crystal electrodes [2 and'l3 may be provided to connect the crystall in'circuit with a vacuum tube oscillation generator 20 as'illustrated in Fig. :3, for example, .toxcontrol the frequency of oscillations thereof. Theparticular oscillator'zZB may. include .a vacuum .tube 2| having-a cathodev22, a ,grid-electrodezland aplateelectrode'z l. The outputcircuit thereof may include a tuning coil 25 connected in parallel circuit relation with a variable: condenser26. A by-pass condenser -21 may connect the mid-point of the tuning coil 25 with the cathode'22. A feedback condenserlt may feed back radio frequency oscillations to the ,grid electrode 23. Suitable batteries as illustrated may be provided .toienergize the cathode 22 and theplate electrode v'24 in a-known: manner. A;.gridleak-resistance :29 and a milliammeter M maybe connected'between'the rid 2-3 and the cathode 22. :It will be understood that the crystal l may beutilizedto control the frequency of oscillat-ionsof any'suitable-zoscillator, the particular oscillator 20 beingshown in Fig. 3as an illustrative example only.

similarly the connectors I'Band l9 mayconnect the crystal I. in circuit withanelectric wave filter system to operate as a selective element thereof.

Figs. 4,-5 ands6 illustrate'respectively top, elevation and end views of a crystal holder .or mounting which:may be utilized for clamping rigidly at the nodes :of motion and establishing electrical connections with the secondharmonic crystal I illustrated in Figs-1 to :3. In vthissarrangement, .two pairs .of coaxial 'metalllc :clamping projections 30,'3I -and32,"33 disposed in contact with the four corresponding crystal ielecill trodes I 0, II, I2 and I3, respectively, and suitably supported from four posts 35 secured to an insulating base 36 by screws 31, for example, may rigidly nodally clamp the crystal I along the central longitudinal axis YY thereof at points or small areas located substantially one-quarter A) the length thereof from the small ends of the crystal l as illustrated in Figs. 1 to 6. The clamping projections 36 and 32 may slide freely in openings in the corresponding supporting posts 35 and be provided with suitable flanges 38 and coil springs 39 to resiliently clamp the crystal I between the clamping projections 39 to 33. The clamping projections 3i and 33 may have suitable screw threads thereon engaging the surfaces of openings in the corresponding supporting posts 35 to adjust the degree of clamping pressure exerted by the springs 39 on the crystal l. Electrical connections between the metallic coated electrodes II, I2 and IE5, I4 respectively, may be indirectly established by conductive connectors 45 and 4! interconnecting the metallic clamping projections 3|, 32 and 3t, 33 respectively, or may be directly established as described and illustrated in connection with the conductors l5 and 56 in Fig. 3. The conductors I8 and I9 may connect the electrodes I 2 and i3, respectively, with an oscillation generator such as the oscillation generator 23 illustrated in Fig. 3, or with any other desired system such as an electric wave-filter system, or other radio apparatus.

Figs. 7 and 8 are top views and Fig. 9 is a side View of another form of holder which may be utilized for mounting and establishing electrical connections with the crystal 5 shown in Figs. 1 to 3. In this arrangement, the crystal I may be supported within a rectangular opening in an insulating block 5% by means of the four fiat electrodes IE! to I3, which may in this instance be pivotally attached to the block 5!! by two pivot pins 5| and 52. Fig. '7 shows the electrodes ID to I3 swung into open position to expose the crystal t. Fig. 8 is a View similar to Fig. 7 but showing the electrodes If! to I3 swung into operative relation with the crystal I. The pin 5i may interconnect the crystal electrodes II and I2 and the pin 52 may interconnect the electrodes IE3 and I3 to excite the second harmonic longitudinal vibration in the length direction Y of the crystal I as illustrated in Fig. 3. Wedge-shaped projections 55 to 58 may be supported by the holder block 50 in any suitable manner and may make contact with small areas of the opposite surfaces of the crystal I on the nodal lines iii-i and 53 thereof, as illustrated in Figs. 1 to 7, hold the crystal I in fixed position between the electrodes It to i3, which may be spaced in close relation to or in contact with opposite electrode surfaces of the crystal I. The projections 55 to 58 may, if desired, be made resiliently adjustable with respect to the holder box 50 to adjust the clampingpressure exerted by the springs on the crystal I at the nodes 59 and 6! thereof. The nodal lines for the crystal I shown in Figs. 1 to 3 are substantially in the positions shown therein. The electrodes III to I3 may be swung about the pivots ill and 52 to open position as illustrated in Fig. 7 to remove or insert the crystal 9.

By giving certain selected values to both the dimensional ratios of width to length and of thickness to length of the crystal I, the longitudinal mode of vibration therein may be mechanically coupled to other modes, as flexures and transverse modes of vibration therein having positive temperature coefficients of frequency, to produce selected negative, positive or zero temperature coeflicients of frequency for the crystal I.

The dimensional ratios ifiandi j to obtain the desired predetermined temperature coefiicient as the zero temperature coefficient of frequency will depend upon the orientation angle 9 of the crystal I and the order of the harmonic operation thereof.

Where the crystal I has an orientation angle or angular position of 9=about +10 degrees rotated about an electric axis X and is excited by an electric field in the direction of the electric axis XX by the two pairs of electrodes I0 to I3 which drive the crystal I at the second harmonic or overtone of the longitudinal vibrations in the direction of the length or longest axis Y, all as illustrated in Figs. 1 to 3, the dimensional ratios and of the crystal i to obtain zero or other predetermined temperature coeiiicient of frequency may be as illustrated by the curves given in Fig. 10.

For example, to obtain zero temperature coefficient of frequency in the second harmonic +10 degree crystal I illustrated in Figs. 1 to 3, the dimensional ratio may be about .28 when the dimensional ratio is about .300 as illustrated in curve A of Fig. 1D; or the dimensional ratio may be about .245 when the dimensional ratio is about .223 as illustrated in curve B of Fig. 10. Curves C and D of Fig. 10 illustrate temperature coefficients of frequency that may be obtained for other values of dimensional ratios It will be noted that crystal apparatus constructed in accordance with this invention by suitable selection of the orientation, mode of vibration and dimensional ratios X Z 'Y, and Y,

may have substantially precisely zero temperature coefficient of frequency or may have a selected positive or negative temperature coeflicient of frequency as illustrated by curves A or B, for example, in Fig. 10.

Fig. 11 shows the values of the frequency constant in terms of kilocycles :13 centimeters of second harmonic +10 degree crystals, as illustrated in Figs. 1 to 3, where one has a dimensional ratio and another has a dimensional ratio =about .30

and both having various dimensional ratios as indicated. The term, frequency constant, as used herein indicates the product of the frequency of the crystal bar I in kilocycles per second and the frequency determining length Y- thereof in centimeters. The curves A and B of Fig. 11 correspond to the curves A and B, respectively, of Fig. 10.

It will be-noted from curves A and B, for eX- ample, in. Figs. 10 and 11 that reducingthe dimensional. ratio as, for example, by reducing the Z dimension of the crystal I while holding the Y. dimension constant, lowers the frequency of the crystal I and at the same time makes the temperature coeificient' of frequency thereof more positive. This property makes it possible to obtain zero temperature coefficient of frequency at any desired frequency, as will be illustrated in connection with Fig. 12' which shows in one graph the approximate relations between the Z dimension, the Y dimension, the frequency and the temperature coefficient of frequency of a second harmonic +10 degree quartz crystal I illustrated in Figs. 1 to. 3, when X=0.22y corresponding to the curve B in Figs. 10 and 11.

Referring to Fig. 12, it Will be noted that reducing the Z dimensions of the crystal I decreases the frequency and, at the same time, makes the temperature coeflicient of frequency more positive; while reducing the Y dimension increases the frequency and, at the same time,

.;,ground to obtain substantially precisely zero temperature ,coeificient of frequency at a desired frequency of 100 kilocycles per second, for example, assuming that the crystal I originally has properties as indicated at point A in Fig. 12. At point A of Fig. 12, the length or Y dimensionof the crystal I is between 61 and 62 millimeters, the width or Z dimension is between 16 and 17 millimeters, and the thickness or X dimension is 0.22Y and at point A the crystal I has a frequency of 95 kilocycles and a temperature coefficient of frequency between 2 and -3 parts per million. per degree centigrade. Reducing the dimension Y to between 58 and 59 millimeters, as indicated at B in Fig. 12, increases the frequency to the selected desired value of 100 kilocycles per second and at the same time makes the temperature coefiicient of frequency more negative, bringing. it to between 4 and 5 parts per million per degree centigrade. Reducing the dimension Z to between 14 and 15 millimeters width for the crystal I as'illustrated at point C in Fig. 12, lowers thefrequency to about 99.4 kilocycles per second and, at the same time, makes-the temperature coefficient of ire quency as illustrated' atpoint E of Fig. 12 may be obtained;

It will be noted: that to obtain the 100 kilocycle zero temperature coefilcient of frequency second harmonic crystal I illustrated at point E of Fig. 12, therlength dimension Y will be about 58.4 millimeters, the width dimension Z Will be about 0-.25-Y, andthe thickness dimension X will be about 0-;22'Y, and that the frequency is given by the relation frequency kilocycles where Y is the length of the crystal I in millimeters.

It will be noted that the orientation, as the +10 degree orientation illustrated in Fig- 1, determines the Wave direction generally in the crystal I. Z and the thickness Xwith respect to the length Y vary the wave direction somewhat and. determine the amounts of coupling to other modes of vibration as flexures and transverse modes having positive temperature coeffi'cient's of frequency in order to produce the desired zero temperature coefficient of frequency for the crystal I.

The control of the temperature coefficient of frequency of the crystal I is such as to produce positive or negative .cloefiicients at will and, therefore, to produce. substantially precisely zero temperature coefii'cient of frequency and the dimensions of the crystal I are largeenoughto insure mechanical strength and contain enough volume of quartz to' store sufficient vibrational energy to insure'strong' oscillations and good-frequency control.

Operation on the second harmonic frequency as illustrated in Figs. 1 to 3 may provide certain.

advantages over operation on the fundamental or the higher order of harmonics as the third,.

fourth, or fifth harmonic, for example.-

When" operated on the second harmonic frequency as'illus'tratedin' Figs. 1' to 3, for example. the crystal I is very active. as an oscillator and maybe operated in an ordinary circuit having.

no additional feedback circuit. As a resonator, the second harmonic operation may offer a great increase in admittance, admittance being. defined? as the ratio'of current to voltage at resonance or the reciprocal of the effective resistance of the.

quency constant, which is the frequency :c the.

length, of the second harmonic crystal l istwice that for the Same crystal vibrated at the fundamental frequency and, therefore, twice. the amount of quartz may be ground off the length dimension Y to change the frequency by a given amount with resulting accuracy in grinding to a specified frequency.

The dimensional ratios of'the Width The arrangement illustrated in Fig. 1 utilizes harmonic operation, orientation, and selected dimensional ratios to produce a crystal suitable for obtaining an extremely accurate frequency, and having a convenient size, a high frequency constant, a high admittance, and two nodal lines or surfaces which may be utilized for rigidly clamping the crystal. Both the frequency and temperature coefiicient of frequency may be raised or lowered separately, insuring a substantially exact adjustment by simple procedure.

While particular dimensional ratios for a particular angular orientation of +10 degrees have been illustrated, it will be understood that the optimum dimensional ratios of width to length and of thickness to length may be similarly obtained in order to secure zero temperature coefiicient of frequency for other angular orientations with respect to the mechanical or Y axis.

While Figs. 1 to 3 illustrate a crystal 1 driven at the second harmonic of its length vibrations substantially in the direction of the Y axis by means of two pairs of interconnected electrodes ID to I3, it will be understood that the crystal may be driven at another harmonic as the third or fourth harmonic of the length vibrations by means of a number of pairs of opposite electrodes similarly interconnected and corresponding in number of pairs to the order of the harmonic desired as, for example, three pairs of opposite electrodes for the third harmonic frequency or four pairs for the fourth harmonic frequency or to drive the crystal at the fundamental length vibrations, one. pair of opposite electrodes may be utilized. When so driven at the fundamental or harmonic longitudinal mode of motion, the zero temperature coefiicient of frequency may be obtained, as in the case of the second harmonic crystal illustrated in Figs. 1 to 3 by a suitable orientation and by selected dimensional ratios I g,- and to couple the longitudinal mode of vibration to other modes having positive temperature c0- eflicients of frequency to produce zero temperature coefficient of frequency as described in connection with the example illustrated.

t will be understood that the crystal I driven at an odd harmonic as, for example, the third, fifth or seventh harmonic may be centrally nodally clamped by a single pair of coaxial clamping projections, and may be utilized as a selective element in an electric wave filter where constancy of frequency is desired independent of substantial temperature change.

Although this invention has been described and illustrated in relation to specific arrangements, it is to be understood that it is capable of application in other organizations and is, therefore, not to be limited to the particular embodiments disclosed but only by the scope of the appended claims and the state of the prior art.

What is claimed is:

1. An elongated piezoelectric quartz crystal of substantially rectangular parallelepiped shape having opposite electrode surfaces and the longest axis thereof disposed substantially perpendicular to an X axis said longest axis being inclined substantially +10 degrees with respect to a Y axis thereof, and means comprising a plurality of pairs of opposite electrodes operatively disposed with respect to said crystal electrode surfaces and interconnections between said electrodes for operating said crystal at the second harmonic frequency of the mode of vibration thereof substantially in the direction of said longest axis, said crystal having selected dimensional ratios of Width and of thickness with respect to said longest axis for mechanically coupling said harmonic mode of vibration to at least one other mode of vibration therein having positive temperature coefiicient of frequency for obtaining zero temperature coemcient of frequency for said crystal, said dimensional ratios being between 0.2 and 0.3.

2. An elongated piezoelectric quartz crystal of substantially rectangular parallelepiped shape having opposite electrode surfaces and the longest axis thereof dispcsed substantially perpendicular to an X axis said longest axis being inclined substantially +10 degrees with respect to a Y axis thereof, and means comprising a plurality of pairs of opposite electrodes operatively disposed with respect to said crystal electrode surfaces and interconnections between said electrodes for operating said crystal at the second harmonic frequency of the mode of vibration thereof substantially in the direction of said longest axis, said crystal having selected dimensional ratios of Width and of thickness with respect to said longest axis and being those determined substantially by the curves of Fig. 10 for mechanically coupling said harmonic mode of vibration to at least one other mode of vibration therein having positive temperature coeflicient of frequency for obtaining a selected temperature coefficient of frequency for said crystal. 3. A piezoelectric quartz crystal element of substantially rectangular parallelepiped shape having its longest axis along a Y axis substantially perpendicular to an X axis and inclined at such an acute angle of substantially +10 degrees with respect to a Y axis thereof, and having such selected dimensional ratios of both the width along a Z axis and the thickness along said X axis thereof with respect to said longest axis as to mechanically couple an overtone frequency of the mode of vibration therein in the direction of said longest axis with another mode of vibration therein for obtaining a selected temperature coeflicient of frequency therefor, said dimensional ratios being those determined substantially by the curves of Fig. 10.

4. The method of adjusting to desired values the temperature coeflicient of frequency and the frequency of a piezoelectric crystal having orthogonal X, Y and Z dimensions the Z dimension making an angle of substantially +10 degrees with respect to the Z axis which includes alternately reducing the Y dimension to such a value as to increase the frequency to the desired value without exceeding the desired value of frequency while making the temperature coefficient of frequency more negative, and reducing the Z dimension to such a value as to make the temperature coefficient of frequency more positive and of the desired value without exceeding the desired value of temperature coefficient of frequency, while decreasing the frequency.

5. An elongated piezoelectric quartz crystal bar of rectangular parallelepiped shape having orthogonal X, Y and Z dimensions of predetermined relative values determined substantially by the curves of Fig. 10, said Z dimension makingan angle of substantially +10 degrees with respect to the Z axis, said Y dimension being reduced to such a value as to obtain the desired frequency for said bar and said 2 dimension being reduced to such a Value as to obtain the desired temperature coefficient of frequency for said bar.

6. A piezoelectric quartz crystal oscillating bar of substantially rectangular parallelepiped shape having orthogonal X, Y and Z dimensions, said Y dimension being elongated, substantially perpendicular to an X axis andinclined substantially degrees with respect to a Y axis, the ratio of said dimensions 2' to Y being substantially .28 and the ratio of said dimensions .X to Y be- -ing,substantially .3 =to'obtainsubstantially zero temperature coefiicient ofirequency when excited at the second harmonic of the longitudinal .mode of vibration in the direction of saidrY di mension-by anelectric field having a component in the direction of-said Xaxis.

7. A piezoelectric quartz crystal oscillating-bar of substantially rectangular parallelepiped shape having orthogonal X, Y and Z dimensions, said Y dimension being elongated,substantially perpendicular to an X axis and-inclined substantially +10 degrees with respect to a Y axis, the ratio of said dimensions-Z to Y being substantially .245 and the. ratio of said dimensions X to .Y being substantially .223 to obtain substantially zero temperature coefficient of frequency when excited at the second harmonic of the longitudinal mode of vibration in the direction of said .Y dimension by an electric field having'a component in thedirection of said X axis.

8. A piezoelectric quartz crystal oscillating bar ofsubstantially rectangular parallelepiped shape having electrode faces-substantially perpendicular to an X axis and having orthogonalX, Y and Z dimensionssaid Y dimension being elongated, substantially perpendicular to said X axis and inclined substantially +10 degrees with respect to the nearest Y axis thereof, the ratio of said X dimension to said Y ,dimension'and the ratio of said-Z. dimension to said iYridimension being selected values between substa-ntially .2 and ;3 to give a predetermined characteristic when :operated-atv the second harmonic *of the longitudinal mode of vibration in the direction of'said Y dimen-sion.

- 9. A piezoelectric oscillating quartz crystal element of substantiallyrectangular parallelepiped shape having electrode faces substantially perpendicular to an Xaxisand having orthogonal X, Y and Z. dimensions; said -.Y dimension being elongated and. inclined at an angle-substantially +10 degrees with respect 'to the nearest Y axis thereof,.said X, Y and zdimensions having such relative proportions *and being those determinedsubstantially by the curves of Fig. 10 as to produce a desired temperature coefiicient of fre- :quency when said crystal is operating at the second harmonic of the longitudinal mode of vibraand Z dimensions, said Y dimension being elongatedand inclined at an angle substantially +10 degrees with respect to the nearest Y axis thereof, said X, Y and Z dimensions having relative proportions determined substantially by the curves of Fig. 10.

11. A piezoelectric quartz crystal oscillator having its axis of greatest length substantially perpendicular to an electric axis and inclined at an acute angle with respect to the optic axis thereof, characterized in this that said angle, and the dimensional, ratios of width to said length and of thickness to said length of said crystal have such relative values as to produce a desired temperature coefiicient of frequency at a given harmonic 'of the longitudinal mode of vibration in the direction of said axis of said length said angle beingsubstantially 80 degrees, said dimensional ratios of width to length and of thickness to length being selected between substantially .2 and .3, and said vibration being the second harmonic of said longitudinal mode of vibration.

12. A piezoelectric crystal element of quartz adapted to vibrate at its second harmonic lengthwise mode of motion having substantially the shape of a rectangular parallelepiped, having its longest or length dimension along a Y axis and having its two other dimensions along an X axis and a Z axis, the orientation of the crystal element being such that the angle between the Z axis and the Z axis is substantially 10 degrees and the dimensions in the X, Y and Z directions being those determined substantially by the curves of Fig. l0.

13. A piezoelectric crystal element of quartz adapted to vibrate at its second harmonic lengthwise mode of motion having substantially the shape of a rectangular parallelepiped, having its longest or length dimension along a Y axis and having its two other dimensions along an X axis and a Z axis, the orientation of the crystal element being such that the angle between the Z axis and the Z axis is substantially +10 degrees and the dimensions in the X, Y and Z directions being those determined substantially by the curves of Fig. 10, said dimension in said Y direction being reduced to such a length as to obtain a desired frequency for said element and said dimension in said Z direction being reduced to such a value as to obtain a desired temperature coeflicient of frequency for said element.

STUART C. HIGHT. 

